Question:
Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (\(u\)) and image distance (\(v\)) using same convex lens having power \(+5\) D as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement.
Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (\(u\)) and image distance (\(v\)) using same convex lens having power \(+5\) D as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement.
Show Hint
Always verify experimental readings using the lens formula to check consistency.
Updated On: Feb 5, 2026
- Readings recorded by \(P_4\) and \(P_5\) persons are incorrect
- Readings recorded by \(P_3\) and \(P_2\) persons are incorrect
- Readings recorded by all persons are correct
- Readings recorded by \(P_3\) persons are incorrect
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Find focal length of the lens.
Given power, \[ P = +5\,\text{D} \Rightarrow f = \frac{1}{P} = 0.2\,\text{m} = 20\,\text{cm} \]
Step 2: Use lens formula.
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Step 3: Check readings one by one.
For \(P_1\): \[ \frac{1}{25} + \frac{1}{96} \approx \frac{1}{20} \] (Correct)
For \(P_2\): \[ \frac{1}{30} + \frac{1}{62} \approx \frac{1}{20} \] (Correct)
For \(P_3\): \[ \frac{1}{35} + \frac{1}{37} \neq \frac{1}{20} \] (Incorrect)
For \(P_4\) and \(P_5\): values satisfy lens formula approximately.
Step 4: Conclusion.
Only \(P_3\) has recorded incorrect readings.
Given power, \[ P = +5\,\text{D} \Rightarrow f = \frac{1}{P} = 0.2\,\text{m} = 20\,\text{cm} \]
Step 2: Use lens formula.
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Step 3: Check readings one by one.
For \(P_1\): \[ \frac{1}{25} + \frac{1}{96} \approx \frac{1}{20} \] (Correct)
For \(P_2\): \[ \frac{1}{30} + \frac{1}{62} \approx \frac{1}{20} \] (Correct)
For \(P_3\): \[ \frac{1}{35} + \frac{1}{37} \neq \frac{1}{20} \] (Incorrect)
For \(P_4\) and \(P_5\): values satisfy lens formula approximately.
Step 4: Conclusion.
Only \(P_3\) has recorded incorrect readings.
Was this answer helpful?
0
0
Top Questions on Ray optics and optical instruments
- In a microscope, the objective has a focal length \(f_o=2\) cm and the eye-piece has a focal length \(f_e=4\) cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is_____.
- JEE Main - 2026
- Physics
- Ray optics and optical instruments
- A collimated beam of light of diameter 2 mm is propagating along the x-axis. The beam is required to be expanded into a collimated beam of diameter 14 mm using a system of two convex lenses. If the first lens has focal length 40 mm, then the focal length of the second lens is_____ mm.
- JEE Main - 2026
- Physics
- Ray optics and optical instruments
- The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___ cm.
- JEE Main - 2026
- Physics
- Ray optics and optical instruments
- A prism of angle $75^\circ$ and refractive index $\sqrt{3$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle angle must be ___. ($\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43$)}
- JEE Main - 2026
- Physics
- Ray optics and optical instruments
A biconvex lens is formed by using two plano-convex lenses as shown in the figure. The refractive index and radius of curvature of surfaces are also mentioned. When an object is placed on the left side of the lens at a distance of \(30\,\text{cm}\), the magnification of the image will be:
- JEE Main - 2026
- Physics
- Ray optics and optical instruments
View More Questions
Questions Asked in JEE Main exam
- Paratrooper jumps... opens parachute after 2s... initial height is ___ m.
- JEE Main - 2026
- Kinematics
- Let \( y = x \) be the equation of a chord of the circle \( C_1 \) (in the closed half-plane \( x \ge 0 \)) of diameter 10 passing through the origin. Let \( C_2 \) be another circle described on the given chord as diameter. If the equation of the chord of the circle \( C_2 \), which passes through the point \( (2, 3) \) and is farthest from the center of \( C_2 \), is \( x + ay + b = 0 \), then \( b \) is equal to:
- JEE Main - 2026
- Coordinate Geometry
- For given vectors \( \vec{a} = -\hat{i} + \hat{j} + 2\hat{k} \) and \( \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \) where \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} = \vec{c} \times \vec{b} \). Then the value of \( (\vec{a}-\vec{b}) \cdot \vec{d} \) is:
- JEE Main - 2026
- Vector Algebra
- Given that \[ \vec a=2\hat i+\hat j-\hat k,\quad \vec b=\hat i+\hat j,\quad \vec c=\vec a\times\vec b, \] \[ |\vec d\times\vec c|=3,\quad \vec d\cdot\vec c=\frac{\pi}{4},\quad |\vec a-\vec d|=\sqrt{11}, \] find $\vec a\cdot\vec d$.
- JEE Main - 2026
- Vector Algebra
- If three vectors are given as shown. If the angle between vectors \( \vec{p} \) and \( \vec{q} \) is \( \theta \), where \[ \cos \theta = \frac{1}{\sqrt{3}}, \quad |\vec{p}| = 2\sqrt{3}, \quad |\vec{q}| = 2, \] then find the value of \[ \left| \vec{p} \times (\vec{q} - 3\vec{r}) \right|^{2} - 3|\vec{r}|^{2}. \]
- JEE Main - 2026
- Vector Algebra
View More Questions